Convergence-Optimal Quantizer Design of Distributed Contraction-Based Iterative Algorithms With Quantized Message Passing
In this paper, the authors study the convergence behavior of distributed iterative algorithms with quantized message passing. They first introduce general iterative function evaluation algorithms for solving fixed point problems distributively. They then analyze the convergence of the distributed algorithms, e.g. Jacobi scheme and Gauss-Seidel scheme, under the quantized message passing. Based on the closed-form convergence performance derived, they propose two quantizer designs, namely the Time Invariant Convergence-Optimal Quantizer (TICOQ) and the Time Varying Convergence-Optimal Quantizer (TVCOQ), to minimize the effect of the quantization error on the convergence.